1. Objective - To solve simple, one-step variable equations
Lesson 2.3 Solving One-step Variable Equations
2:3 Solving One-Step Variable Equations
Objective - To solve simple, one-step variable equations
What is an equation?
Equation - a balanced statement of equality
between two quantities.
4 + 3 = 7
4 + 3 7 =
fulcrum
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
Algebra 1 by James Wenk © 2003 published by TEACHINGpoint

2. 4 + 3 7 =
- 3
fulcrum
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

3. 4 = 7
fulcrum
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

4. 4 = 7
fulcrum
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

5. 4 = 7
fulcrum
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

6. 4 + 3 7 =
- 3
- 3
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

7. 4 4 = Perform the same operation to both sides
to keep the equation balanced.
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

8. This property can be used to solve variable equations.
x + 6 11 = -6 -6 x 5 =
Algebraic Approach
x + 6 = 11
x = 5
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

9. Solve. 1) m + 2 = 10 4) m - 4 = 9 -2 -2 +4 +4 m = 8 m = 13
m = 8
m = 13
2) x - 4 = 6
5) 11 = x + 2
x = 10
9 = x
3) x + 7 = 3
6) 8 + y = -6
x = -4
y = -14
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

10. Rules for Solving Equations
1) Goal: Isolate the variable.
2) Undo operations with their opposite operation.
3) Always do the same thing to both sides of the equation.
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

11. Solve. 1) -4 + x = 15 4) - 4 = m + 9 +4 +4 -9 -9 x = 19 -13 = m
x = 19
-13 = m
2) 7 = x + 13
5) = x
16 = x
-6 = x
3) -10 = 6 + x
6) y =
y = -5
-16 = x
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

12. Solve. 1) 5x = 35 3) 9 = -3m 5 5 -3 -3 x = 7 -3 = m 2) 4) (-6) (-6)
x = 7
-3 = m 2) 4)
(-6)
(-6)
-72 = x
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

13. -4k = 14 -4 -4 Acceptable Answers All answers must be fully reduced!
All answers must be fully reduced!
There is nothing improper about an improper fraction!
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

14. Solve. 1) 7x = 16 3) 9 = -m 7 7 (-1)9 = -m(-1) -9 = m 2) 4) (-4) (-4)
(-1)9 = -m(-1)
-9 = m 2) 4)
(-4)
(-4)
(-2)
(-2)
k = 16
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

15. Solving Equations Involving Fractions
Long Way
Short Way
Easier to multiply
by the reciprocal!
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

16. Solve. 1) 3) 2) 4)
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series